On the stability of self-similar blow-up for C1,α solutions to the incompressible Euler equations on R3

Tarek M. Elgindi; Tej Eddine Ghoul; Nader Masmoudi

doi:10.4310/CJM.2021.v9.n4.a4

On the stability of self-similar blow-up for C^1,α solutions to the incompressible Euler equations on R³

Tarek M. Elgindi, Tej Eddine Ghoul, Nader Masmoudi

Research output: Contribution to journal › Article › peer-review

Abstract

We study the stability of recently constructed self-similar blow-up solutions to the incompressible Euler equation. A consequence of our work is the existence of finite-energy C^1,α solutions that become singular in finite time in a locally self-similar manner. As a corollary, we also observe that the Beale-Kato-Majda criterion cannot be improved in the class of C^1,α solutions.

Original language	English (US)
Pages (from-to)	1035-1075
Number of pages	41
Journal	Cambridge Journal of Mathematics
Volume	9
Issue number	4
DOIs	https://doi.org/10.4310/CJM.2021.v9.n4.a4
State	Published - 2021

ASJC Scopus subject areas

General Mathematics

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10.4310/CJM.2021.v9.n4.a4

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AB - We study the stability of recently constructed self-similar blow-up solutions to the incompressible Euler equation. A consequence of our work is the existence of finite-energy C1,α solutions that become singular in finite time in a locally self-similar manner. As a corollary, we also observe that the Beale-Kato-Majda criterion cannot be improved in the class of C1,α solutions.

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On the stability of self-similar blow-up for C^1,α solutions to the incompressible Euler equations on R³

Abstract

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